I checked a 1957 Offical Railroad Guide and came out, roughly, not exactly, to something ltike this:
Burlington route 18 trains
Milwaukee route 19 trains
Gulf Mobile & Ohio 6 trains
Pennsylvania RR. 9 trains.
This is counting each train as one--not twice as in both in bound and outbound. To add outbound and inbound together would of course double the above numbers. There may have been commuter operations in addition to the above. Never lived there, I do not know Chicago as a resident would.
Other major long distance stations in Chicago, in addition to Union, were Dearborn, Grand Central, Central, La Salle Street and Chicago and Northwestern.